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Magnetism and Peierls distortion in Dirac semimetal CaMnBi$_2$

Aashish Sapkota, Niraj Aryal, Xiao Hu, Masaaki Matsuda, Yan Wu, Guangyong Xu, John M. Wilde, Andreas Kreyssig, Paul C. Canfield, Cedomir Petrovic, John M. Tranquada, Igor A. Zaliznyak

TL;DR

This work resolves the origin of the resistivity and optical anomalies in CaMnBi$_2$ by showing a coupled structural and magnetic transition at $T^{*} \approx 46$ K from tetragonal $P4/nmm$ to orthorhombic $Pcmn$. Polarized and unpolarized neutron diffraction, together with X-ray diffraction, reveal a zigzag bond-order-wave distortion in the Bi square-net layer (a Peierls-type instability), with unit-cell doubling along $c$ but only minimal changes to Mn antiferromagnetism. DFT calculations support the experimental finding that the distortion is electronically driven and Berry-Dirac band–related, predicting small energy gains and subtle band-structure modifications consistent with a partial Peierls gap along the distortion direction while preserving Dirac features. Overall, CaMnBi$_2$ hosts an electronically driven two-dimensional Peierls transition in its Dirac square-net, rather than a bulk TRS-breaking Weyl state from spin canting, with implications for tuning Dirac semimetals via band filling and lattice distortions.

Abstract

Dirac semimetals of the form $A$Mn$X_2$ ($A =$ alkaline-earth or divalent rare earth; $X =$ Bi, Sb) host conducting square-net Dirac-electron layers of $X$ atoms interleaved with antiferromagnetic Mn$X$ layers. In these materials, canted antiferromagnetism can break time-reversal symmetry (TRS) and produce a Weyl semimetallic state. CaMnBi$_2$ was proposed to realize this behavior below $T^{*}\sim 50$ K, where anomalies in resistivity and optical conductivity were reported. We investigate single-crystal CaMnBi$_{2}$ using polarized and unpolarized neutron diffraction, x-ray diffraction, and density functional theory (DFT) calculations to elucidate the underlying crystal and magnetic structures. The results show that the observed anomalies do not originate from spin canting or weak ferromagnetism; no measurable uniform Mn spin canting is detected. Instead, CaMnBi$_2$ undergoes a coupled structural and magnetic symmetry-lowering transition at $T^{*} = 46(2)$ K, from a tetragonal lattice with C-type antiferromagnetism to an orthorhombic phase with unit-cell doubling along the $c$ axis and minimal impact on magnetism. Analysis of superlattice peak intensities and lattice distortion reveals a continuous second-order transition governed by a single order parameter. The refined atomic displacements correspond to a zigzag bond-order-wave (BOW) modulation of Bi-Bi bonds, consistent with an electronically driven Peierls-type instability in the Dirac-electron Bi layer, long anticipated by Hoffmann and co-workers [W.~Tremel and R.~Hoffmann, \textit{J. Am. Chem. Soc.} \textbf{109}, 124 (1987); G.~A.~Papoian and R.~Hoffmann, \textit{Angew. Chem. Int. Ed.} \textbf{39}, 2408 (2000)]. %\textcite{TremelHoffman_JACS1987} [JACS {\bf 109}, 124 (1987)].

Magnetism and Peierls distortion in Dirac semimetal CaMnBi$_2$

TL;DR

This work resolves the origin of the resistivity and optical anomalies in CaMnBi by showing a coupled structural and magnetic transition at K from tetragonal to orthorhombic . Polarized and unpolarized neutron diffraction, together with X-ray diffraction, reveal a zigzag bond-order-wave distortion in the Bi square-net layer (a Peierls-type instability), with unit-cell doubling along but only minimal changes to Mn antiferromagnetism. DFT calculations support the experimental finding that the distortion is electronically driven and Berry-Dirac band–related, predicting small energy gains and subtle band-structure modifications consistent with a partial Peierls gap along the distortion direction while preserving Dirac features. Overall, CaMnBi hosts an electronically driven two-dimensional Peierls transition in its Dirac square-net, rather than a bulk TRS-breaking Weyl state from spin canting, with implications for tuning Dirac semimetals via band filling and lattice distortions.

Abstract

Dirac semimetals of the form Mn ( alkaline-earth or divalent rare earth; Bi, Sb) host conducting square-net Dirac-electron layers of atoms interleaved with antiferromagnetic Mn layers. In these materials, canted antiferromagnetism can break time-reversal symmetry (TRS) and produce a Weyl semimetallic state. CaMnBi was proposed to realize this behavior below K, where anomalies in resistivity and optical conductivity were reported. We investigate single-crystal CaMnBi using polarized and unpolarized neutron diffraction, x-ray diffraction, and density functional theory (DFT) calculations to elucidate the underlying crystal and magnetic structures. The results show that the observed anomalies do not originate from spin canting or weak ferromagnetism; no measurable uniform Mn spin canting is detected. Instead, CaMnBi undergoes a coupled structural and magnetic symmetry-lowering transition at K, from a tetragonal lattice with C-type antiferromagnetism to an orthorhombic phase with unit-cell doubling along the axis and minimal impact on magnetism. Analysis of superlattice peak intensities and lattice distortion reveals a continuous second-order transition governed by a single order parameter. The refined atomic displacements correspond to a zigzag bond-order-wave (BOW) modulation of Bi-Bi bonds, consistent with an electronically driven Peierls-type instability in the Dirac-electron Bi layer, long anticipated by Hoffmann and co-workers [W.~Tremel and R.~Hoffmann, \textit{J. Am. Chem. Soc.} \textbf{109}, 124 (1987); G.~A.~Papoian and R.~Hoffmann, \textit{Angew. Chem. Int. Ed.} \textbf{39}, 2408 (2000)]. %\textcite{TremelHoffman_JACS1987} [JACS {\bf 109}, 124 (1987)].

Paper Structure

This paper contains 26 sections, 3 equations, 20 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Structure and Physical Properties of CaMnBi$_2$
  3. Experimental Details
  4. Experimental Results and Analysis
  5. Bulk Properties
  6. Néel-type Antiferromagnetic Order
  7. Absence of Measurable Uniform Spin Canting
  8. $L = 0.5$ Superlattice Reflections
  9. X-Ray Diffraction Measurements: Tetragonal to Orthorhombic Transition
  10. Polarized Neutron Diffraction Evidence for Structural and Magnetic Superlattice Order
  11. Symmetry of the $Pcmn$ Distortion
  12. Refinement of Crystal and Magnetic Structures by Polarized and Unpolarized Neutron Diffraction
  13. DFT Analysis of Crystal Structure and Electronic Properties
  14. Total Energy of Competing Lattice Distortions
  15. Effect of Lattice Distortion on Electronic Band Structure
  16. ...and 11 more sections

Figures (20)

  • Figure 1: Crystal and magnetic structures of CaMnBi$_{2}$ across three temperature regimes: (right) tetragonal paramagnetic phase ($P4/nmm$) for $T > T_\mathrm{N}$; (center) tetragonal C-type antiferromagnetic phase ($P4^\prime /n^\prime m^\prime m$) for $T_\mathrm{N} > T > T^{*}$; (left) orthorhombic C-type antiferromagnetic phase ($Pc^\prime m^\prime n^\prime$) with $Pcmn$ symmetry for $T < T^{*}$. While $Pnma$ is the conventional setting for orthorhombic 112 compounds, we adopt the non-standard $Pcmn$ setting here to maintain axis orientation and labeling consistent with the high-temperature $P4/nmm$ tetragonal structure. In the right two panels, the shaded region indicates the Bi square lattice that hosts Dirac bands, which becomes zig-zag distorted in the orthorhombic $Pcmn$ phase shown in the leftmost panel.
  • Figure 2: Temperature dependence of the magnetic susceptibility, $\chi(T) = M(T)/H$, (a) and normalized resistivity, $\tilde{\rho} = \rho(T)/\rho(\mathrm{300~K})$ (left scale), and its derivative, $d\tilde{\rho}/dT$ (right scale), (b) of CaMnBi$_{2}$. Panel (a) shows zero-field-cooled susceptibility measured with an applied field of $\mu_0 H = 1$T for $\mathbf{H} \parallel \mathbf{c}$ and $\mathbf{H} \parallel \mathbf{a}$ Characteristic temperatures $T_\mathrm{N}$, associated with magnetic ordering, and $T^*$, discussed as a possible spin reorientation in Ref. Corasaniti_2019, are indicated in the susceptibility and resistivity plots, respectively.
  • Figure 3: Evolution of the (1, 0, 0) magnetic Bragg peak with temperature from unpolarized (a) and polarized (spin-flip channel) (b) neutron diffraction measurements. The slight red-shift in peak position upon warming results from thermal expansion. (c) Temperature dependence of the integrated magnetic intensity from unpolarized (triangles) and polarized (squares) measurements. The magnetic intensity for the unpolarized data was obtained by subtracting the average intensity above $T_\mathrm{N}$, treated as a non-magnetic background. The two datasets are cross-normalized to overlay. The solid blue line is a fit to a critical-type power law, $I \sim (T_{\mathrm{N}} - T)^{2\beta}$.
  • Figure 4: (a) The $(0, 0, 2)$ lattice Bragg peak measured at four different temperatures above and below $T^{*}$, showing no apparent enhancement at low temperature. (b) Temperature dependence of the integrated intensity of the $(0, 0, 2)$ peak up to 120 K. The gray line represents a linear fit to the measured data, while the colored lines indicate the expected changes due to a ferromagnetic contribution, calculated for canting angles $\alpha = 2^\circ$ (orange), $5^\circ$ (magenta), and $10^\circ$ (green).
  • Figure 5: Temperature dependence of the $(1, 0, 0.5)$ superlattice peak in CaMnBi$_{2}$. (a)–(c) Intensity contour plots from $(H, 0, L)$ mesh scans measured at three temperatures: $T < T^{*}$ (8 K), $T^{*} < T < T_\mathrm{N}$ (70 K), and $T > T_\mathrm{N}$ (315 K), respectively. (d) One-dimensional (1D) scans through $(1, 0, 0.5)$ along the $[H, 0, 0]$ direction at three representative temperatures. Solid lines are fits to a Gaussian lineshape. (e) Temperature dependence of the integrated intensity obtained by fitting 1D scans to Gaussian profiles, as shown in (d). The solid line is a fit to the power law $I(T) \propto (1 - T/T_\mathrm{N})^{2\beta}$, with $\beta = 0.24(2)$.
  • ...and 15 more figures